On second thought I realize something. You might have a file that has no endnote style. In that case you need to add the endnote style. (The easiest way to do that that I can see, is to copy it out of some other document.)

phspaelti is right, probably the file you are working with lacks an "Endnote" style. As suggested you can copy-paste (or drag-drop) one in. Ideally Nisus Writer should provide a way to add such a style automatically- I believe it's filed as a feature enhancement, but I'll make sure.

Thanks to you both. This makes sense, and indeed the problem was solved when I added an Endnote style to the document. Now clicking on the green star yields both options (when earlier it had only one).